Solving the sampling problem of the Sycamore quantum circuits

Abstract

We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a new method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in obtaining a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with $53$ qubits and $20$ cycles, we have generated one million uncorrelated bitstrings $\{\mathbf s\}$ which are sampled from a distribution $\hat P(\mathbf s)=|\hat \psi(\mathbf s)|^2$, where the approximate state $\hat \psi$ has fidelity $F\approx 0.0037$. The whole computation has cost about $15$ hours on a computational cluster with $512$ GPUs. The obtained one million samples, the contraction code and contraction order is made public. If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware.